Back with heavy CRT TVs, everyone placed them on a cabinet or solid shelf .... and yes injuries happened if it was knocked over or just suddenly fell.
Many modern lighter LCD TVs are more often hung on a wall. Yes they are lighter but they are also heavier than hanging a painting so it needs reinforced bolts to go in the wall. Many people hire professionals to do this but most people I know do it themselves. Some people are better with things like this than others. Which is why I've seen many TVs just fall off because they were installed wrong.
An improperly wall-mounted LCD isn't a huge falling threat unless there's a child or pet under it though.
I would expect most injuries from tube tvs would be muscle related from lifting them, with the occasional severe shock from those who were brave enough to open them up for repairs but not smart enough to discharge them properly.